Real Options and Regulation

Gordon Sick

Professor of FinanceHaskayne School of Business

University of Calgarysick@ucalgary.ca

January 2008

A Car Leasing Puzzle

ñ Why are daily rental rates for a car from a rental agencylike Hertz significantly greater than the per diemequivalent of the monthly rate?

ñ Someone renting a car on a daily basis has the flexibilityof only having to rent the car when and where it isneeded. This flexibility option is valuable, so the renteris willing to pay a higher daily rate.

The Fama-French Puzzle

ñ Fama and French found that the Capital Asset PricingModel (CAPM) beta had no explanatory power incross-sectional share returns.

ñ But, they found significant return premia for size andmarket-to-book, even though CAPM provides notheoretical basis for this.

ñ Small firms and firms with low market-to-book ratiosusually have a lot of growth options. Options have agreat deal of operating leverage.

ñ The operating leverage causes their betas to varyinversely with their market value, but the CAPM testsassume their betas are constant.

ñ Thus, the Fama-French factors are merely good proxiesfor the time-varying betas of firms with real options.

Another Puzzle: The NPV Investment Policy

ñ The NPV of a project is the present value (PV) ofprojected benefits net of costs.

ñ The NPV rule says “Go ahead with a capital project if andonly if it has a positive NPV”.

The NPV Rule

Value

PV ofBenefits (Variable)

PV of Costs (fixed)

RejectProject

AcceptProject

Theory vs Application

ñ The theory says we should accept a project with a $1billion capital cost if it has an NPV of $1.

ñ Why don’t firms accept such projects?

ñ A bond trader will often do a round trip transaction thatearns 10 basis points. That is, they would transact $1million of bonds to earn an NPV of $1000.

ñ But, most companies would reject a $1 million capitalproject that only has an NPV of $10,000 or even$100,000.

Real Options

Real options arise when the decision maker has flexibility oroptionality in investment decisions. The real option decisionto invest generally involves a tradeoff:

Risk gives incentives to defer a project. The realoption separates upside potential from downsiderisk. The manager waits to collect moreinformation, so when there is more risk, there ismore delay.

Dividends provide an incentive to develop a project early.Measuring dividends in a real option setting canbe complex, but in many real options, it is thefree cash flow payout from a developed project.

Analyzing Real Options

Suppose the real option has an underlying asset of valuePV of Benefits ≡ P , which follows a stochastic process.Real option value W (P) depends on two things:

1. Terminal conditions for the value of the real option whenthe underlying risk driver P assumes specific values,such as 0,∞ or an exercise (development) point.

2. Some methodology for extending option values to allpossible values of P :

ñ Lattice or tree models.ñ Solution of the fundamental valuation PDE from asset

pricing theory.ñ Monte Carlo methods, extended to least squares Monte

Carlo methods if the option can be exercised early.

The Real Options Investment Decision

Value

PV ofBenefits

P

K P*

RejectProject

AcceptProject

Real Option ValueW(P)

The Real Options Investment Decision

ñ The real options model determines a hurdle value P∗

and the decision rule is to defer development as long asP is below P∗.

ñ The optimal time for development is the first time that Prises above P∗.

Terminal Conditions:Criteria Defining the Hurdle P∗

Value Matching The real option value equals the NPV whenP = P∗. The real option gains its value from thefact that at some point, the real option will beexercised and the project will be developed.

Smooth Pasting The real option graph is tangent to the NPVgraph at P∗. This tangency criterion is similar tothe criteria in other constrained optimizationproblems whereby an optimum is characterizedby the tangency between the contours of theobjective function and the contours of theconstraint function — Kuhn Tucker or Lagrangemultipliers.

Real Option Value vs NPV

ñ The real options hurdle price is higher than the NPVhurdle: P∗ > K . Thus, projects are optimally developedlater under the real options rule.

ñ The real option value exceeds NPV.

ñ The real option value is non-negative. The real optionprotects its owner from achieving a negative value.

ñ In effect, the real option separates upside potential fromdownside risk by deferring development until theunderlying PV of Benefits is sufficiently above thedevelopment cost to greatly reduce the potential for loss.

Value Lost by Investing Too Early

Value

PV ofBenefits

P

K P*P**

Value Destroyed by Bad Policy

Value Lost by Investing Too Early

ñ Suppose the firm adopts a decision rule that it willdevelop as soon as the PV of Benefits, P , equals P∗∗

where K < P∗∗ < P∗.

ñ The value matching condition holds because the realoption value is anchored to the NPV value at the time ofdevelopment.

ñ But, the smooth pasting tangency criterion for optimalitydoes not hold.

ñ The resulting value function lies below the optimal realoption value, but above the NPV graph.

Modifying the NPV Rule to IncludeOpportunity Cost of Extinguishing a Real Option

Value

PV ofBenefits

P

K P*

Real Option ValueW(P)

Modified NPV= (Old NPV) – W(P)

W(P*)= P* – K

Modifying the NPV Rule to Reflect theOpportunity Cost of Extinguishing a Real Option

ñ If we charge the opportunity cost of the extinguishedreal option against the NPV calculation, we get theModified NPV rule shown in the blue curve, which showsOld NPV−W (P).

ñ Including this opportunity cost allows us to return to thedecision rule “Invest as soon as the Modified NPV rises to0 from a negative value”.

Book Value and Market Value

Consider a firm (or division) that has a single asset, namelythe real option.

ñ Market value is formed from market assumptions of thebehaviour of the managers in their dynamic developmentpolicies. If the market has reason to believe thatmanagement cannot or will not follow the optimaldevelopment policy, it will bid down the market value.

ñ Accounting principles do not allow the firm to book thevalue accruing from a prospective dynamic strategy.Thus, book value is based on past decisions only, andnot future strategy.

Book Values are Related to the NPV Rule

ñ Prior to development (P < P∗), the book value of thedivision is 0, but the market value is the value of the realoption, W (P) > 0.

ñ Development requires an injection of capital in theamount K .Immediately after development (P = P∗), the book valueis the invested capital, K , and the market value is P = P∗.

ñ Thus, at the time of development, the Market-to-BookRatio is P∗

K >> 1.

Market-to-book Ratios and Tobin’s Q Ratio

ñ In this simple model, the replacement cost of the assetsafter development is K , so the Market-to-book ratioequals Tobin’s Q ratio.

ñ Thus, firms that have a lot of real (growth) options havea high Q, where Q >> 1.

Economic Rent and Real Options

ñ Economic rent also generates conditions where Q > 1.

ñ Thus, firms that own real growth options have someappearance of earning economic rent.

ñ This becomes an important issue if a regulated entity hasreal options: how should tariffs be set?

Setting Tariffs in the Presence of Real Options

ñ In the development option above, the replacement costof the assets and the book value of the assets is K , butthe investment requires the owner to extinguish a realoption that had a value of W (P∗) = P∗ − K at the time ofdevelopment.

ñ Logically, any tariff for use of the developed asset shouldinclude compensation for the value of the extinguishedoption.

ñ One approach is to include the value of the option in thecost base for the tariff. Thus, the cost base would beP∗ = P∗ − K + K , rather than replacement cost K .

ñ Another approach is to increase the allowable rate ofreturn on the lower cost base of K . This is consistentwith the fact that unregulated corporations have internalrates of return that are significantly higher than theirweighted average cost of capital.

The Regulatory Objective:Avoid Distorting Investment Incentives

ñ If the regulator only allows the recovery of capital costsK at the cost of capital used to calculate NPV, theregulated entity has no incentive to optimally invest, andperhaps no incentive to invest at all.

ñ The infrastructure provider would rationally change itsbehaviour by reducing investment activity if it were toanticipate that it would not be compensated for the realoptions.

ñ If investment did occur, but there is no compensation forthe value of extinguished real options, a subsidy is givento either the final consumer or access seekers.

Dividends or Convenience Value

ñ We have seen that the basic real option to delayinvestment involves a tradeoff between delaying toresolve risk and investing to capture a dividend payoff.

ñ Sometimes this dividend is characterized as aconvenience dividend. Convenience dividends arisewhen a good has a high value only if it is available forimmediate delivery. The immediacy could arise from ashock to the market that generates larger demand ordiminished alternative supply.

ñ Convenience dividends for commodities can bemeasured from forward curves when there isbackwardation: lower forward prices for longer terms.

ñ Electric power has very volatile convenience dividends.The owner of a gas-fired power generator captures theconvenience value of positive electricity price shocks.

Excess Capacity as a Real Option

ñ Convenience value arises from a real option itself.

ñ The convenience value of a good arises from the realoption to use the good when its value rises because of ademand shock. This assumes that the good takes timeto build and cannot be instantly supplied in unlimitedquantities when a price shock arrives.

ñ In general, if a capital asset takes time to build and thereare shocks to the profit stream it can produce, there aregood real-option reasons to invest earlier to generateexcess capacity.

ñ The excess capacity can be used to quickly ramp upproduction and capture positive shocks to profit, just asthe electricity producer captures peaks in electricityprices.

Facilities Access Regulation

ñ Facilities access is a system whereby regulation of theallowable consumer prices to be charged by aninfrastructure provider is replaced by regulation of thecost of access to the production system. This allowsmultiple vendors to buy the production and sell it toconsumers in a competitive market.

ñ Facilities access has been used around the world to“deregulate” telecom, electric power, natural gas andother utilities. From a consumer perspective, theseindustries were deregulated, but in reality, the regulationwas transferred from the consumer level to a wholesalelevel.

Facilities Access Tariffs and Capacity Options

ñ We have seen that a non-distorting tariff to be paid to ainfrastructure provider who has the option to delayinvestment must include compensation for theopportunity cost of the real option that is extinguishedto make the investment.

ñ Similarly, it is important to determine a non-distortingaccess tariff system when there are real options,including options to carry excess or latent capacity.

Facilities Access Tariffs when Capacity is Finite

ñ Sometimes there are hard limits to the amount ofcapacity that can be used.

ñ For example, a refinery, railway or shipping port has alimited capacity. If access is granted to a seeker, itdisplaces the ability of the provider to use the excesscapacity at a later date for its own real options.

ñ If this is coupled with a stochastic risk driver that createsreal options, the regulator has an extremely difficult taskin designing a non-distorting tariff system.

Facilities Access Tariffs when Capacity is Finite:Single-Part Tariff

ñ Suppose the regulator sets an access tariff that is paidmonthly or annually, once access is attained.

ñ This gives the access seeker a free option to gain accessif its product markets achieve high profit margins, but toavoid paying the fixed cost of building capacity if theproduct markets have low profit margins.

ñ The infrastructure provider does not know how muchexcess capacity to build because it does not knowwhether or not a seeker will actually come to use thecapacity.

ñ Moreover, if the seeker is in the same output market asthe provider, the seeker will ask for excess capacityexactly when the infrastructure provider needs it for itsown use.

Facilities Access Tariffs when Capacity is Finite:Single-Part Tariff

ñ Suppose the single-part tariff will only be received by theprovider when the seeker actually starts to use thecapacity. Then, the provider does not receive anycompensation at the time it invests in the capacityoption, so it has an incentive to underinvest in capacity.

ñ The regulator could set a high single-part tariff tocompensate the provider on an ex ante basis for thepossibility of access being granted.

ñ But, there is a limit to how high the tariff can be setwithout it becoming a deterrent for the seeker to actuallydemand the capacity.

Facilities Access Tariffs when Capacity is Finite:Single-Part Tariff

ñ Indeed, setting a very high single-part tariff may fail toinduce infrastructure investment because the provideranticipates that access will be actually sought only with avery low probability.

ñ Also, there is no mechanism for credibly committing topaying the high tariff once the access is sought. Once theexcess capacity is in place, the access seeker could arguethat the marginal cost of supplying the excess capacity islow, since the capital costs are sunk. The regulatormight be persuaded to lower the tariff to marginal cost,preventing the provider from recovering the capital costsof setting aside the excess capacity for the seeker.

Facilities Access Tariffs when Capacity is Finite:Two-Part Tariff

ñ To address the problems with a single-part tariff, theregulator could set an up-front fee to be paid when theaccess seeker nominates or reserves capacity.

ñ In order for the provider to know how much excesscapacity to build for a seeker, this up-front fee wouldhave to be paid at the time the provider builds excesscapacity. Otherwise, the provider will under-provideexcess capacity.

ñ In this situation, the access is provided to the newcapacity, rather than the existing capacity that theinfrastructure provider had built for its own use.

ñ The seeker would still pay an annual fee for capacityused, once it actually gains access to the capacity.

Regulating Access in the Presence of Real Options isNot an Easy Task

We can see that the regulator faces a significant task indesigning a non-distorting facilities access system in thepresence of real options.

ñ It must identify all the real options available to theinfrastructure provider and the access seeker.

ñ It must model and value these real options. Or, it coulddesign a regime where the seeker pays a maximal fee(e.g. all prospective capital costs) up front. But, thiscould be a significant deterrent to access.

ñ It must design a system in which tariffs are paid at thepoints in time when real option decisions are made, inorder to provide incentives to build the optimal size andat the optimal time.

ñ The regulator must set the tariff levels at least to reflectthe real option value, which depends on the prospectivecosts of investment, as well as the stochastic nature ofthe processes driving the real option.

ñ To support timely decision making, this analysis needsto be done in a short period of time, despite the fact thatit is done in a confrontational regulatory environment.

ñ A simple cost base and cost of capital system will resultin distorted incentives because it is a single-part tariff.

ñ Building a proper access regulatory system wouldrequire methods not yet developed in any jurisdiction.